When did Artificial Intelligence research first start?
The earliest research into thinking machines was inspired by a confluence of ideas that became prevalent in the late 30s, 40s and early 50s (e.g. formal logic, automata, robots). Although the Turing test was proposed in the 1950s by Alan Turing, the work culminated back in the 1940s in the invention of the programmable digital computers, an abstract essence of mathematical reasoning. These ideas were inspired by a handful of scientists from a variety of fields who began seriously considering the possibility of building an electronic brain. The field of artificial intelligence research was officially founded as an academic discipline in 1956 during the Dartmouth workshop.
However, the concept of artificial beings is not new and it's as old as the Greek myths of Hephaestus and Pygmalion, which incorporated the idea of intelligent robots (such as Talos) and artificial beings (such as Galatea and Pandora).
See the following articles at Wikipedia for further details:

Artificial intelligence (AI)
History of artificial intelligence
Timeline of artificial intelligence